Monday, October 31, 2016

224: Did America Fail a Math Test?

Well, we’ve made it to another election season here in the US. Among other things, it means that we’re once again hearing from politicians all over the spectrum about how they will fix American education, if we only vote for them. We also start hearing all the stories that show how we are failing currently at education. One of the more amusing ones that has been making the rounds again in the story of the ill-fated Third Pounder hamburger. Supposedly a competing restaurant chain introduced a Third Pounder, which was designed to beat McDonald’s famous Quarter Pounder, but it failed in the marketplace. The root cause of the failure was apparently that the average American didn’t understand that a third is greater than a quarter, and thought they were being ripped off. This story has a bit of the ring of an urban legend to it though— don’t most people successfully cut up pizzas and follow kitchen recipes that require us to have at least this basic knowledge of fractions? So I decided to do a little browsing on the web and see if I could get the real story.

Although it sounds suspicious, an article from Mother Jones, a generally well-researched periodical, seems to lend credibility to the legend. The Third Pound burger was introduced in the 1980’s by fast food chain A&W, one of the many lesser competitors to the great McD, It did indeed fail in the marketplace, and according to the Mother Jones article, they tracked down a statement by a former company owner, Alfred Taubman about what happened. Here’s the quote they got:

Well, it turned out that customers preferred the taste of our fresh beef over traditional fast-food hockey pucks. Hands down, we had a better product. But there was a serious problem. More than half of the participants in the Yankelovich focus groups questioned the price of our burger. "Why," they asked, "should we pay the same amount for a third of a pound of meat as we do for a quarter-pound of meat at McDonald's? You're overcharging us." Honestly. People thought a third of a pound was less than a quarter of a pound. After all, three is less than four!

So, does this definitively prove that we are living in a nation of morons who think that 1/3 is less than 1/4? Not so fast. For one thing, this is not a summary of actual data at the time, but a recollection from years later. We all know how those can be colored subconsciously by rumors and personal inclinations as time passes. Like most prominent businessmen, Taubman wanted to believe that he did everything right, and it was the cruel universe that denied him his earned victory. Perhaps one focus group participant made such a comment, and it stewed in his mind for years after. Personally, I’ve always preferred McDonald’s burgers over A&W, regardless of what the A&W CEO thinks about their inherent superiority over “traditional fast-food hockey pucks.”

A thread at snopes.com brings up a few more interesting arguments. Remember that the value provided is the pre-cooked weight of the burger. Depending on the grinding process, ground beef can vary widely in content and quality. Fat and water are lost during cooking, so the comparative post-cooking weights of the quarter and third pounders from different chains cannot be taken for granted. Also, there may be other binding ingredients in the patty— so even if the weights are comparable, one may have more actual beef than the other. And we can’t forget one other factor, the fact that it often seems more natural to deal in quarters than thirds; threes are an odd number, harder to subdivide and work with in many contexts. So the term “quarter pounder” may just trigger more comfortable feelings when you read it on a menu, for reason that you don’t consciously consider.

So, is our nation really so ignorant of basic fractions that we reject 1/3-pound burgers for being smaller than quarter pounders? I think the jury is still out. McDonald’s has actually introduced several 1/3-pound specialty burgers in recent years, but it’s hard to separate their performance from the general 21st-century decline in our taste for fast food. A site called adventuresinfrugal,com implicitly proposes an interestting experiment: someone should introduce both third pounder and fifth pounder burgers at the same price, and see which sell better. Perhaps that would finally tell us whether or not our nation is truly confused about basic fractions.

Note that this podcast is intended mainly for audio consumption, so you will not see the numerous illustrations & diagrams you would find at most math sites, though these are linked in the show notes whenever possible.

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